In particular, I custom-designed a multiple-choice test, intended to measure an individual's mathematical ability, while minimizing the reliance on previously acquired knowledge.
Also, I put together a two page "cheat sheet", which outlined all the necessary concepts to successfully complete the exam, without providing any explicit answers.
Most importantly, "cheat sheets" proved significantly more beneficial (in terms of improved test performance) to those students who were more likely to have had a secondary education of lower quality.
This result has important implications for educational policies in Chile and elsewhere, suggesting that a transition to ability-focused admission tests would facilitate the access to higher education for talented students from disadvantaged backgrounds.
Also, although there are some differences across degrees and secondary school types, in general undergraduate students are more likely to be dismissed, and have lower grades, when they share their first semester college class with a secondary schoolmate.
Moreover, students assigned to first semester college classrooms with a higher concentration of classmates who attended the same secondary school(s) generally have significantly lower grades, and are less likely to graduate.
Finally, students sharing their first semester college classroom with students from public or subsidized secondary schools are more likely to be dismissed due to poor academic performance.
The fact that these peer effects are persistent In time points to the existence of a path dependence pattern, suggesting that this initial period in college is key for student adaptation.
These findings have important implications for the design of policies intended to improve the adaptation of freshman college students and the access to higher education, suggesting that students would benefit from targeted first semester college class group assignment policies, as well as from additional transitional aid tailored to their profiles.
The second chapter addresses the question of how to distinguish "knowledge" from "ability", in the context of improving the access to higher education.